While transport in conjugated polymers has many similarities to that in crystalline inorganic materials, several key differences reveal the unique relationship between the morphology of polymer films and the charge mobility. We develop a model that directly incorporates the molecular properties of the polymer film and correctly predicts these unique transport features. At low degree of polymerization, the increase of the mobility with the polymer chain length reveals trapping at chain ends, and saturation of the mobility at high degree of polymerization results from conformational traps within the chains. Similarly, the inverse field dependence of the mobility reveals that transport on single polymer chains is characterized by the ability of the charge to navigate around kinks and loops in the chain. Lastly, these insights emphasize the connection between the polymer conformations and the transport and thereby offer a route to designing improved device morphologies through molecular design and materials processing.